Gamma-ray Large Area Space Telescope

Gamma-ray Large Area Gamma-ray Large Area Space TelescopeSpace Telescope

Intra-Tower Tracker Alignment

Michael Kuss

INFN Pisa

Instrument Analysis Workshop 4SLAC

15 July 2005

Instrument Analysis Workshop 4, SLAC, 15 July 2005 Michael Kuss2

Towers …Towers …

the ideal tower

a horizontal shift

a vertical shift

a rotation

the real tower


Class ResidualClass Residual

Class Residual is used for alignment:

Residual(const TString="MyRootFile.root", const TString="residual.root", const TString geo="");

~Residual() { delete myEvent; delete myTracker; }

void Go(int lastEntry=-1);

// general for DrawXxx: residual is h_abs - h_abs_ext// ***********// draws the residual, top without fitting, bottom with gauss fitvoid DrawResidual(TString plane, TCut="");// draws top the slope vs. residual, bottom the profile with pol1 fitvoid DrawResSlope(TString plane, TCut="");// draws top the other coordinate vs. residual, bottom profile with pol1 fitvoid DrawResOrd(TString plane, TCut="");// draws the slope profiles for all planesvoid DrawResSlopeAll(TCut="abs(h_abs_ext-h_abs)<1");// draws the ordinate profiles for all planesvoid DrawResOrdAll(TCut="abs(h_abs_ext-h_abs)<1");// attempt to do a "statistical" (not event be event) correction of rotZ of// planes. 2x3 histograms. Left uncorrected, right rotZ corrected. Top// ordinate vs. residual, middle profile of that, bottom residual.void DrawResOrdCorr(TString plane, TCut="");


What does it do?What does it do?

aligns planes horizontally, along the measured coordinate

aligns planes vertically

does an estimate of the rotation around z

What does it not do?

doesn’t align planes horizontally, parallel to the strips

doesn’t determine rotations around x and y


General ProcedureGeneral Procedure

user> source cmt/setup.shuser> rh9_gcc32opt/runTreeMaker.exe digi.root recon.root ”” tree.rootuser> rootroot [0] .x compile.Croot [1] Residual* r = new Residual(”tree.root”,”res.root”,”geo.txt”)

… opens tree.root for reading, res.root for writing, and reads the geometry from geo.root.

root [2] r->Go()

... reads events from the tree file. Fits a straight tracks, discarding the clusters of both planes of the tray to which the plane to be studied belongs. For each cluster(!), fills a small tree with

plane name measured horizontal position of cluster (vertical to the strips) measured vertical position of cluster (i.e., elevation of the plane) extrapolated horizontal position of cluster vertical to the strips (track fit) extrapolated horizontal position of cluster parallel to the strips (track fit in the other view) inverse slope of track

and saves the small tree in the residual file.

root [3] r->Draw...() // e.g. r->DrawResSlopeAll()

utilizes one of the Draw... methods. And saves a new geometry to disk.


selecting tracksselecting tracks


ResidualResidual

r->DrawResidual(”X5”, ”abs(h_abs-h_abs_ext)<1”)

horizontal displacement: 59m


Residuals vs. slope (horizontal and vertical Residuals vs. slope (horizontal and vertical alignment)alignment)

Aligns:• horizontal ( to strips)• vertical

r->DrawResSlope(”Y9”, ”abs(h_abs-h_abs_ext)<1&&abs(invSlope)<1”)

X4

X3

X2

X1

X0

realposition

idealposition

res = x + z · cot(θ)

θ


vertical displacement: 81m


Residuals vs. slope of track (all planes)Residuals vs. slope of track (all planes)

r->DrawResSlopeAll()


Residuals vs. position in other viewResiduals vs. position in other view

X

Y, ideal position

Y, real position

r->DrawResOrd(”Y9”, ”abs(h_abs-h_abs_ext)<1”)


rotation around z: 0.54mrad


Residuals vs. position in other view (all planes)Residuals vs. position in other view (all planes)

res_x%y res_x-p0-y*p1%yr->DrawResOrdAll() r->DrawResOrdCorr(”Y9”)


Alignment resultsAlignment results


How To AlignHow To Align

Alignment is an iterative process.

Before RA v8r3p1:

• run with 10k events till convergence




initially, convergence was defined as maximum deviation of any parameter of two consecutive geometries to be less than 10μm (but not more than 5 iterations)

1 iteration for 100k events takes about 1h CPU

Since RA v8r3p1:

• run with 100k events till “real” convergence

“reaI” convergence is achieved if a geometry repeats (but not more than 50 iterations)

1 iteration for 100k events takes about 6 min CPU

result is “perfect” geometry


1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19

-0.600-0.575-0.550-0.525-0.500-0.475-0.450-0.425-0.400-0.375-0.350-0.325-0.300-0.275-0.250-0.225-0.200-0.175-0.150-0.125-0.100-0.075-0.050-0.0250.0000.0250.0500.0750.1000.1250.1500.1750.2000.2250.250

Alignment verticalY0

X0

X1

Y1Y2

X2

X3

Y3

Y4

X4

X5

Y5

Y6

X6

X7

Y7

Y8

X8

X9

Y9

Y10

X10

X11

Y11

Y12

X12

X13

Y13

Y14

X14

X15

Y15

Y16

X16

X17

Y17

iteration

posi

tion/

mmAlignment: 1Alignment: 1stst try try


Intra-Tower Alignment BlindnessIntra-Tower Alignment Blindness

AttentionIntra-tower alignment is blind versus:

• translation

• shearing

• vertical scaling (horizontal is fixed by strip dimensions)

• rotation

• translation of the planes of one view vs. the other

• rotation of the planes of one view vs. the other

After every iteration, separately in each view, I “correct” for:

• ∑posh = 0 (horizontal translation)

• ∑posh22 min. (shearing)

• ∑(posv-posv,ref) = 0 (vertical translation)

• ∑(posv-posv,ref)2 min. (vertical scaling)

• ∑rotz = 0 (rotation around z)


1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19

-0.150

-0.140

-0.130

-0.120

-0.110

-0.100

-0.090

-0.080

-0.070

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.100

Alignment verticalY0

X0

X1

Y1Y2

X2

X3

Y3

Y4

X4X5

Y5

Y6

X6

X7

Y7

Y8

X8

X9

Y9

Y10

X10

X11

Y11

Y12

X12

X13

Y13

Y14

X14

X15

Y15

Y16

X16

X17

Y17

iteration

posi

tion/

mmAlignment: 3Alignment: 3rdrd try try


Gle

am3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

-0.300

-0.280

-0.260

-0.240

-0.220

-0.200

-0.180

-0.160

-0.140

-0.120

-0.100

-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

Alignment vertical

Y0X0X1Y1Y2X2X3Y3Y4X4X5Y5Y6X6X7Y7Y8X8X9Y9Y10X10X11Y11Y12X12X13Y13Y14X14X15Y15Y16X16X17Y17

iteration

posi

tion/

mm

11stst 100k 100k


13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

-0.090

-0.085

-0.080

-0.075

-0.070

-0.065

-0.060

-0.055

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

Alignment vertical

-0.0850.0210.000-0.049-0.0250.0010.000-0.0060.015-0.002-0.0200.0210.042-0.009-0.0110.0610.055-0.0080.0070.0490.0260.0030.0000.0360.0230.0050.004-0.004-0.0170.0100.006-0.039-0.043-0.003-0.005-0.060

iteration

posi

tion/

mm

11stst 100k 100k


13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

-0.043

-0.040

-0.038

-0.035

-0.033

-0.030

-0.028

-0.025

-0.023

-0.020

-0.018

-0.015

-0.013

-0.010

-0.008

-0.005

-0.003

0.000

0.003

0.005

0.008

0.010

0.013

0.015

0.018

0.020

0.023

0.025

0.028

0.030

0.033

0.035

Alignment vertical

-0.0150.0070.032-0.0100.0000.0030.0150.0210.011-0.001-0.0250.006-0.004-0.021-0.015-0.014-0.001-0.009-0.002-0.0060.001-0.010-0.0120.0050.004-0.0080.0000.0160.0010.0130.0180.0030.0020.017-0.002-0.021

iteration

posi

tion/

mm

22ndnd 100k 100k


13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

-0.055

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085

Alignment vertical

-0.0100.0740.032-0.005-0.0080.008-0.0030.0150.008-0.013-0.0070.0100.017-0.031-0.0320.010-0.008-0.036-0.042-0.011-0.018-0.029-0.015-0.013-0.009-0.017-0.0030.001-0.0040.0080.0240.0050.0060.0450.0380.009

iteration

posi

tion/

mm

33rdrd 100k 100k


13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

-0.055-0.053-0.050-0.048-0.045-0.043-0.040-0.038-0.035-0.033-0.030-0.028-0.025-0.023-0.020-0.018-0.015-0.013-0.010-0.007-0.005-0.0020.0000.0030.0050.0080.0100.0130.0150.0180.0200.0230.0250.0280.0300.0330.0350.0380.0400.0430.0450.0480.0500.053

Alignment vertical

-0.018-0.031-0.042-0.012-0.002-0.033-0.0060.0100.0210.0080.045-0.0020.0010.0130.0190.0130.0060.0170.0300.001-0.0060.0220.032-0.0120.0040.0280.0130.0010.008-0.007-0.032-0.004-0.007-0.048-0.029-0.002

iteration

posi

tion/

mm

44thth 100k 100k


13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

-0.095

-0.090

-0.085

-0.080

-0.075

-0.070

-0.065

-0.060

-0.055

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

Alignment vertical

-0.0860.0530.056-0.072-0.0240.021-0.0020.0180.068-0.035-0.0290.0270.045-0.035-0.0400.0100.028-0.037-0.0060.0260.042-0.022-0.0100.0280.0070.000-0.0070.0150.0000.0120.020-0.015-0.0450.0380.024-0.071

iteration

posi

tion/

mm

55thth 100k 100k


Reproducibility: verticalReproducibility: vertical

absolute position / mm deviation / umplane #0 #1 #2 #3 #4 avg #0-avg #1-avg #2-avg #3-avg #4-avgY0 42.610 42.581 42.587 42.612 42.605 42.599 11 -18 -12 13 6X0 44.710 44.702 44.692 44.701 44.689 44.699 11 3 -7 2 -10X1 74.402 74.383 74.373 74.394 74.377 74.386 16 -3 -13 8 -9Y1 76.751 76.743 76.749 76.753 76.750 76.749 2 -6 0 4 1Y2 106.519 106.523 106.528 106.523 106.515 106.522 -3 1 6 1 -7X2 108.935 108.928 108.925 108.931 108.922 108.928 7 0 -3 3 -6X3 139.620 139.630 139.617 139.627 139.619 139.623 -3 7 -6 4 -4Y3 141.939 141.948 141.949 141.932 141.936 141.941 -2 7 8 -9 -5Y4 172.693 172.712 172.719 172.693 172.702 172.704 -11 8 15 -11 -2X4 175.042 175.053 175.047 175.047 175.056 175.049 -7 4 -2 -2 7X5 205.807 205.818 205.819 205.816 205.822 205.816 -9 2 3 0 6Y5 208.114 208.117 208.117 208.107 208.114 208.114 0 3 3 -7 0Y6 238.896 238.890 238.899 238.899 238.897 238.896 0 -6 3 3 1X6 241.340 241.342 241.347 241.332 241.342 241.341 -1 1 6 -9 1X7 271.278 271.288 271.295 271.294 271.303 271.292 -14 -4 3 2 11Y7 273.549 273.548 273.543 273.544 273.546 273.546 3 2 -3 -2 0Y8 303.407 303.417 303.408 303.418 303.413 303.413 -6 4 -5 5 0X8 305.911 305.904 305.928 305.912 305.924 305.916 -5 -12 12 -4 8X9 335.807 335.809 335.823 335.813 335.822 335.815 -8 -6 8 -2 7Y9 338.141 338.143 338.135 338.137 338.138 338.139 2 4 -4 -2 -1Y10 368.078 368.083 368.074 368.082 368.082 368.080 -2 3 -6 2 2X10 370.465 370.464 370.479 370.458 370.467 370.467 -2 -3 12 -9 0X11 400.355 400.361 400.373 400.353 400.369 400.362 -7 -1 11 -9 7Y11 402.788 402.794 402.778 402.785 402.792 402.787 1 7 -9 -2 5Y12 432.712 432.729 432.716 432.724 432.724 432.721 -9 8 -5 3 3X12 435.026 435.023 435.031 435.018 435.032 435.026 0 -3 5 -8 6X13 464.999 465.005 465.004 465.006 465.002 465.003 -4 2 1 3 -1Y13 467.349 467.353 467.346 467.346 467.349 467.349 0 4 -3 -3 0Y14 497.369 497.372 497.364 497.366 497.368 497.368 1 4 -4 -2 0X14 499.649 499.647 499.648 499.648 499.640 499.646 3 1 2 2 -6X15 529.678 529.682 529.673 529.683 529.674 529.678 0 4 -5 5 -4Y15 532.019 532.011 532.017 532.014 532.011 532.014 5 -3 3 0 -3Y16 561.970 561.957 561.975 561.972 561.968 561.968 2 -11 7 4 0X16 564.241 564.234 564.215 564.232 564.218 564.228 13 6 -13 4 -10X17 594.272 594.263 594.247 594.271 594.258 594.262 10 1 -15 9 -4Y17 596.707 596.691 596.712 596.704 596.701 596.703 4 -12 9 1 -2 STDEV: 6


Reproducibility: horizontalReproducibility: horizontalabsolute position / mm deviation / um

plane #0 #1 #2 #3 #4 avg #0-avg #1-avg #2-avg #3-avg #4-avgY0 -0.064 -0.062 -0.054 -0.051 -0.053 -0.057 -7 -5 3 6 4X0 -0.068 -0.072 -0.076 -0.070 -0.076 -0.072 4 0 -4 2 -4X1 -0.089 -0.087 -0.097 -0.092 -0.097 -0.092 3 5 -5 0 -5Y1 -0.070 -0.070 -0.067 -0.067 -0.068 -0.068 -2 -2 1 1 0Y2 -0.023 -0.025 -0.024 -0.025 -0.023 -0.024 1 -1 0 -1 1X2 0.129 0.134 0.125 0.128 0.129 0.129 0 5 -4 -1 0X3 0.124 0.126 0.122 0.126 0.124 0.124 0 2 -2 2 0Y3 0.153 0.147 0.149 0.148 0.147 0.149 4 -2 0 -1 -2Y4 0.153 0.147 0.151 0.149 0.149 0.150 3 -3 1 -1 -1X4 0.126 0.129 0.132 0.129 0.133 0.130 -4 -1 2 -1 3X5 0.115 0.114 0.119 0.117 0.120 0.117 -2 -3 2 0 3Y5 -0.078 -0.077 -0.080 -0.081 -0.082 -0.080 2 3 0 -1 -2Y6 -0.042 -0.040 -0.046 -0.047 -0.046 -0.044 2 4 -2 -3 -2X6 -0.090 -0.092 -0.086 -0.089 -0.087 -0.089 -1 -3 3 0 2X7 -0.082 -0.086 -0.075 -0.084 -0.078 -0.081 -1 -5 6 -3 3Y7 -0.052 -0.048 -0.054 -0.055 -0.053 -0.052 0 4 -2 -3 -1Y8 -0.032 -0.031 -0.035 -0.035 -0.032 -0.033 1 2 -2 -2 1X8 -0.071 -0.072 -0.064 -0.072 -0.067 -0.069 -2 -3 5 -3 2X9 -0.119 -0.121 -0.115 -0.118 -0.117 -0.118 -1 -3 3 0 1Y9 0.111 0.115 0.106 0.109 0.112 0.111 0 4 -5 -2 1Y10 0.142 0.144 0.142 0.141 0.144 0.143 -1 1 -1 -2 1X10 -0.081 -0.083 -0.077 -0.085 -0.080 -0.081 0 -2 4 -4 1X11 -0.108 -0.105 -0.102 -0.107 -0.104 -0.105 -3 0 3 -2 1Y11 -0.106 -0.102 -0.104 -0.104 -0.104 -0.104 -2 2 0 0 0Y12 -0.105 -0.105 -0.105 -0.104 -0.105 -0.105 0 0 0 1 0X12 0.045 0.045 0.045 0.043 0.046 0.045 0 0 0 -2 1X13 0.035 0.034 0.035 0.035 0.037 0.035 0 -1 0 0 2Y13 -0.018 -0.018 -0.016 -0.015 -0.019 -0.017 -1 -1 1 2 -2Y14 -0.026 -0.026 -0.026 -0.023 -0.029 -0.026 0 0 0 3 -3X14 0.016 0.016 0.011 0.013 0.013 0.014 2 2 -3 -1 -1X15 0.005 0.004 0.000 0.002 0.002 0.003 2 1 -3 -1 -1Y15 0.017 0.016 0.019 0.019 0.017 0.018 -1 -2 1 1 -1Y16 0.023 0.023 0.025 0.025 0.025 0.024 -1 -1 1 1 1X16 0.072 0.074 0.066 0.072 0.071 0.071 1 3 -5 1 0X17 0.041 0.043 0.038 0.046 0.036 0.041 0 2 -3 5 -5Y17 0.016 0.011 0.019 0.016 0.020 0.016 0 -5 3 0 4

STDEV: 2


The Future of LeaningTowerThe Future of LeaningTower

•can only analyze single tower runs

•introduces ambiguities for the resulting geometry

•doesn’t iterate on rotations

•people don’t like it anyway

merge with AlignmentContainer


Intra-Tower Alignment Blindness (revisited)Intra-Tower Alignment Blindness (revisited)

Intra-tower alignment is blind versus:

• translation

• shearing

• vertical scaling (horizontal is fixed by strip dimensions)

• rotation

• translation of the planes of one view vs. the other

• rotation of the planes of one view vs. the other


TranslationTranslation

Intra-tower alignment:

absolute position of a single tower is ambiguous

Inter-tower alignment:

tracks passing tower gaps fix the relative positions

SOLVEDSOLVED


RotationRotation

Intra-tower alignment:

rotation of a single tower with respect to some coordinate system is ambiguous

Inter-tower alignment:

tracks passing tower gaps fix the rotation of one tower vs. the others

SOLVEDSOLVED


ShearingShearing

There is no way to correct for shearing from data!

Metrology measurements?

Average over all towers?

Do we care? 50μm vs 554mm for a perpendicular track = 0.1 mrad


Vertical ScalingVertical Scaling

There is no way to correct the vertical scale from data!

Metrology measurements?

Average over all towers?

Do we care? 70μm vs 554mm for a 45° track = 0.1 mrad

Documents

Gamma-ray Large Area Space Telescope